Concentrated flux interior permanent magnet (CFIPM) motors have the advantage that their utilization of flux linkage is more efficient than that of general IPM motors and CFIPM motors are suitable for washing machine motors, which demand lowspeed, hightorque specifications. However, low efficiency occurs in the lowspeed hightorque mode considering the highspeed operation for spin mode. This paper proposes a magnet overhang structure between the rotor core that reduces leakage flux and improves efficiency for a CFIPM in wash mode. Optimization of the 3D design of magnet overhang structures is performed to improve the efficiency with the same quantity of permanent magnets. The validity of the optimal design is experimentally verified through the fabrication of prototypes.
1. Introduction
Recently in the washing machine market, there has been increased in requests for large washing capacity and high efficiency. To accomplish this, motor design focuses on washing machine motors that will improve powerdensity and high efficiency.
The operation of a washing machine motor is divided into two modes. One is wash mode, with lowspeed and hightorque, and the other is spin mode, with highspeed and lowtorque. Therefore a washing machine motor should be designed to take the characteristics of both these different operating modes into account. Compared to the highspeed mode, the lowspeed, hightorque mode has a relatively low efficiency. In addition, the recent demand for larger washing capacity increases the load torque in the wash mode, ensuring that the wash mode has low efficiency and low outpower. The price limit of the washing machine is constrained by the price of the washing machine motor, which in turn limits the quality of raw material that can be used for the motor. In most cases, only aluminum wires and ferrite magnets can be used. With these materials, it is difficult to improve efficiency in the wash mode with its lowspeed and hightorque. Therefore, the shape of the washing machine motor must be chosen to improve the power density and efficiency.
The inductances of the daxis and qaxis of interior permanent magnet (IPM) motors are different. Thus, IPM motors can use the reluctance torque in addition to the magnet torque
[1
,
2]
. Thus the entire torque of these motors is higher than that of surface permanent magnet (SPM) motors, which only use the magnet torque. Accordingly, IPM motors have been extensively researched for systems requiring high power density and high efficiency
[3]
.
Concentrated flux IPM (CFIPM) motors have a different rotor structure that can concentrate the flux, compared to conventional IPM motors. In CFIPM motors, the amount of useful flux linkage can be maximized. Therefore, the efficiency and the power density of CFIPM motors can be improved
[4

7]
and CFIPM motors should be suitable for the wash mode of a washing machine
To increase the power density of CFIPM motors for a washing machine, the number of poles should be increased. However, poles may have large leakages because they are close to the distance between the rotor cores, and the rotor core size is smaller than that of a structure with a low pole number. This reduces the efficiency of the wash mode.
This study proposes a magnet overhang structure between the rotor core and the magnet that reduces leakage flux and improves the efficiency of the wash mode. The magnet overhang structure means that the magnet height is greater than the rotor core height. Furthermore with design optimization of the magnet overhang structure, we maximize the efficiency of the CFIPM motor
[10
,
11]
. The optimization variables are the dimensions of the magnet and rotor core. We use two optimization approaches: the Kriging model based on Latin hypercube sampling (LHS) and a genetic algorithm (GA)
[12

15]
. The optimal results from the optimization algorithm are verified with 3Dfinite element analysis (FEA). To confirm the analysis and the optimal design results, the optimal model has been manufactured and tested.
2. CFIPM Motor
 2.1 Configuration and specification
Home appliances such as the washing machine use multipolar structured CFIPM motors, which can be modeled with innerrotortype structures and concentratedwinding type stators.
Fig. 1
shows a CFIPM motor, where the permanent magnet has been magnetized in a concentrated flux direction.
Structure of the CFIPM motor
The specifications of the CFIPM motor are listed in
Table 1
. The stator and the rotor have an overhang, so that the stator is longer than the rotor cores. However the lengths of the rotor core and magnet are the same. In this study, overhang structures are not applied to the model.
Specification of basic model
Specification of basic model
Fig. 2
shows the backelectromotive force (BackEMF) of the basic model, which is 45.62 Vrms.
BackEMF of a basic model (at 150 rpm)
 2.2 Proposed magnet overhang
In terms of the effective flux linkage, CFIPM motors have an advantage because the rotor cores and magnets are arranged to concentrate the flux structure. As the number of poles increases, the distances between magnets and rotor cores as well as their sizes decrease, which then cause the leakage flux to increase. Leakage fluxes in concentrated flux structures with high pole numbers have various paths. A major leakage flux path exists on the upper and lower sides, as shown in
Fig. 3(a).
These leakage fluxes reduce the efficiency. To reduce the leakage flux, we propose a magnet overhang on the rotor core, as shown in
Fig. 3(b)
.
Leakage flux by overhang structure
A magnet overhang is applied as a rotor core that is 1 mm longer than the fixedheight magnet on both the upper and lower sides, as shown in
Fig. 3(b)
. To confirm the effect of the overhang, the leakage flux is calculated for Region 1, shown in
Fig. 3(b)
, both in the cases of no overhang and a 1mm overhang. As shown in
Table 2
, the leakage flux decreased by 12.3%, due to the magnet overhang between the magnet and rotor core. This shows the relationship between magnet overhang and leakage flux. Therefore, the heights of the magnet and rotor core are established as optimization design variables to determine the optimal size for the magnet overhang.
Characteristics of magnetic overhang
Characteristics of magnetic overhang
3. Optimal Design
 3.1 Optimal design of the CFIPM motor
A flow chart of the optimization strategy is shown in
Fig. 4.
First, objective functions and constraints are defined. Then, sampling points is established in accordance with the design of experiment (DOE). Next, the approximation modeling is performed using the Kriging technique and the GA. Finally, the optimal values of the design variables are obtained.
Optimization process
The Kriging model has stronger linearity than the traditional response surface method (RSM) and thus accurate approximation modeling functions of nonlinear data can be obtained using this model. In addition, to improve the accuracy of the Kriging model that is highly dependent on data, the Latin hypercube sampling (LHS) technique is used as a DOE
[16
,
17]
. The LHS makes experimental points into a matrix consisting of n lines and k columns and arranges individual lines as experimental points where n is the number of levels and k is the number of design variables. In particular, the characteristics of the LHS are that when creating design points, overlapping between experimental points and that the LHS can be easily implemented
[18]
.
 3.2 Objective functions, constrains and design variables
The objective function is the maximum efficiency. The RMS value and the total harmonic distortion (T.H.D) characteristic of BackEMF are established as constraints so that the operating characteristics would not be lower than those of the basic model. The weights of the rotor cores and magnets which are closely related to the material costs are established as constraints.
• Objective function:
Maximize: Efficiency
• Constraints:

BackEMF (RMS) > 46.0Vrms, T.H.D < 3.15%

Rotor cores weight < 1.5kg

Magnet weight = 0.875kg
The design variables for optimization are shown in
Fig. 5.
The height of the stator is fixed at 23 mm and the number of permanent magnets is specified as that of the basic model. Design variables are established to determine the optimal point of the overhang structure at which leakage flux would be minimized. Design variable X1 is the height of the rotor core, X2 is the height of each permanent magnet, X3 is the length of each permanent magnet, and X4 is the width of each permanent magnet. Since the same volume of permanent magnets is used, the height of the magnet (X2) is determined based on X3 and X4. Since the combinations of the design variables determine the physical distances of leakage flux that occur between the rotor core and the magnet, the optimal design point, where the leakage flux is minimized, can be determined.
Optimization process
The ranges of the design variables for the optimal design are as follows:
• Design variables:

X1 (Rotor height): 23 mm < X1 <29 mm

X2 (Magnet height): 25 mm < X2 < 32 mm

X3 (Magnet length): 16 mm < X3 <20 mm

X4 (Magnet width): 6 mm < X4 <8 mm
 3.3 Optimal design results
To maximize the efficiency, design variables are established as X1, X2, X3, and X4. As shown in
Table 3
, the analysis results for each variable by DOE show the relationship between design variables and the objective function.
The analysis results for each variable by DOE
The analysis results for each variable by DOE
Using the GA, we determined an optimal design point that satisfied both the objective function and the constraints.
Fig. 6
shows the convergence of the objective function and constraints using the GA. The individual design variables converged on an optimal design point.
Convergence progress of the subject function
The optimal values of the design variables are calculated by the convergence processes, as shown in
Fig. 7
.
Dimensions of the basic model and optimal model
The analysis results of the 3D characteristics of the optimal model are shown in
Table 4
. The BackEMF is improved over the basic model by 2.2%, and the phase current is decreased, thus the efficiency is improved from 41.5% to 42.8%, whereas the normal range of efficiency of a washing machine is 3040% due to the washing mechanism. These results show that the leakage flux is reduced and the amount of flux linked to the stator is increased. In addition, the T.H.D is improved by 1.5%.
Characteristics of the basic model and optimal model
Characteristics of the basic model and optimal model
4. Experiment
The validity of the optimal design is verified through fabricating and experimenting on the prototype.
Fig. 8
shows a prototype of the optimized CFIPM motor.
The optimized CFIPM motor
The BackEMF of the optimal prototype model is shown in
Fig. 9
and
Fig. 10
shows the torqueefficiency curve at wash mode. As shown in
Table 5
, the experimental results of the prototype confirmed the analysis results of the characteristics in the optimal model.
BackEMF of the prototype (at 150 rpm)
TorqueEfficiency curve of the prototype
Analysis and experiment results of optimal model
Analysis and experiment results of optimal model
5. Conclusion
In this paper, we proposed a magnet overhang structure to reduce leakage flux and consequently improve the efficiency of CFIPM motors with high pole numbers. Optimization of the 3D design is performed and as shown in
Table 6
. The result showed improvement of the Back EMF by 2.2% over the basic model, with a 2.0 point improvement in efficiency. In addition, by fabricating and experimenting with the prototype model, we confirmed that the actual efficiency is improved.
Comparison of the basic and prototype model
Comparison of the basic and prototype model
Acknowledgements
This research was supported by BK21PLUS program through the National Research Foundation of Korea funded by the Ministry of Education.
BIO
ByungIl Kwon He received his B.S. and M.S. degrees in Electrical Engineering from Hanyang University, Korea and his Ph.D. in Electrical Engineering from Tokyo University, Japan. He is currently a Professor at Hanyang University. His research interests are linear drive systems, numerical analysis of electric machines and motor control.
KeunYoung Yoon He received his B.S. and M.S. degrees in Electronics Engineering from Hanyang University in 2003 and 2005. He is currently an Engineer at Samsung Electronics.
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